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From: Mark Shore on 7 Jun 2010 07:55
TideMan <mulgor(a)gmail.com> wrote in message <b2eb37a4-0b03-4f38-a284-86738ae54be8(a)z15g2000prh.googlegroups.com>...
....
> This is NOT the way to do it.
> Search on "phase randomisation" in this forum and you'll get an
> algorithm that does exactly what you want, but in the proper
> (numerically robust) way.

For some reason, I needed to use the advanced search option since the simple MATLAB Central search box did not return the referenced page.
From: Erwin on 7 Jun 2010 12:26
TideMan <mulgor(a)gmail.com> wrote in message <b2eb37a4-0b03-4f38-a284-86738ae54be8(a)z15g2000prh.googlegroups.com>...
> This is NOT the way to do it.
> Search on "phase randomisation" in this forum and you'll get an
> algorithm that does exactly what you want, but in the proper
> (numerically robust) way.

Hello,

Thanks for your reply!
Well, I've searched this forum and couldn't really find a response to what i want to implement...
I need to generate a Power Spectrum which follows a f^(-beta) law, and then have this in the time domain.

What's really wrong with the code I've put in a previous message?

Thanks again for your help, you're all very kind!
From: dbd on 7 Jun 2010 14:16
On Jun 6, 7:22 pm, "Erwin " <car...(a)gmail.com> wrote:
> ...
> now i have a function Y(i) that has real and complex values, and plotting abs(Y).^2 versus de frequency it gives me what i want...
>
> my doubt here, is: now how to get the equivalent function in time?!
....

When you have gotten this far, you can implement the last two dashed/
indented points in the first column on page 709 in your paper by:

1) allocate a length 2*N+2 array of zeros

2) fill the array with Y starting with the second element going
forward

3) fill the array from the last element forward with the complex
conjugate of Y (this is where ifft expects the negative frequency data
to be, in reverse order)

4) ifft the array

5) discard the imaginary component

The result of the ifft will be a complex array but the imaginary
component should consist only of roundoff error. Save the real part as
the time series.

Dale B. Dalrymple

From: Greg Heath on 7 Jun 2010 16:08
On Jun 7, 12:26 pm, "Erwin " <car...(a)gmail.com> wrote:
> TideMan <mul...(a)gmail.com> wrote in message <b2eb37a4-0b03-4f38-a284-86738ae54...(a)z15g2000prh.googlegroups.com>...
> > This is NOT the way to do it.
> > Search on "phase randomisation" in this forum and you'll get an
> > algorithm that does exactly what you want, but in the proper
> > (numerically robust) way.
>
> Hello,
>
> Thanks for your reply!
> Well, I've searched this forum and couldn't really find a response to what i want to implement...
> I need to generate a Power Spectrum which follows a f^(-beta) law, and then have this in the time domain.
>
> What's really wrong with the code I've put in a previous message?
>
> Thanks again for your help, you're all very kind!

The power law you state is just an asymptotic approximation
that is not valid near zero frequency, Therefore, you
should not just blindly use ifft and expect to find a
discrete sampling of a nonpathological square integrable
time function.

Why not try something like (-pi*Fs <= w=2*pi*f < pi*Fs)

abs(X) = a^(b/2)/(w^2+ a^2)^(b/4), b > 1.

Although specified probability distributions could be
generated, is is sufficient, without those specifications,
to just choose a phase that is uniformly distributed
over [0, 2*pi].

Hope this helps,

Greg


From: Erwin on 7 Jun 2010 16:17
dbd <dbd(a)ieee.org> wrote in message <60c6c697-8145-4eb2-8f49-c89c2f06ef04(a)z15g2000prh.googlegroups.com>...
> On Jun 6, 7:22 pm, "Erwin " <car...(a)gmail.com> wrote:
> > ...
> > now i have a function Y(i) that has real and complex values, and plotting abs(Y).^2 versus de frequency it gives me what i want...
> >
> > my doubt here, is: now how to get the equivalent function in time?!
> ...
>
> When you have gotten this far, you can implement the last two dashed/
> indented points in the first column on page 709 in your paper by:
>
> 1) allocate a length 2*N+2 array of zeros
>
> 2) fill the array with Y starting with the second element going
> forward
>
> 3) fill the array from the last element forward with the complex
> conjugate of Y (this is where ifft expects the negative frequency data
> to be, in reverse order)
>
> 4) ifft the array
>
> 5) discard the imaginary component
>
> The result of the ifft will be a complex array but the imaginary
> component should consist only of roundoff error. Save the real part as
> the time series.
>
> Dale B. Dalrymple

Hello Dale,

Let me see if I understood what you've said.

So I should create a new array, starting with a zero, followed by the values I created, and after them, I plug the complex conjugate of these values, and end with a zero?

After I do the ifft, the size of the array is the (double + 2) of the one I created before, then how to I create the time function now? There are still imaginary components, but they aren't close to zero..

Thanks a lot!
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